Question

The population density is approximately ___ people per square mile?

Answer 1

Concept:

The formula for the population density is given below as

`\text{Population density=}\frac{population}{\text{area}}`

The population given in the question is

`\text{population =12,620}`

Step 1:

To figure out the area of the shape, we will divide the shape into two parts as given in the image below

The area of part A will be calculated below as

`\begin{gathered} A_a=l* b \\ l=40mi+25mi=65mi \\ b=60mi-25mi=35mi \\ A_a=65mi*35mi=2275mi^2 \end{gathered}`

The area of part B will be calculated below as

`\begin{gathered} A_B=l* b \\ l=25mi \\ b=25mi \\ A_B=l* b=25mi*25mi=625mi^2 \end{gathered}`

Hence,

The total area of the township will be

`\begin{gathered} A=A_A+A_B \\ A=2275mi^2+625mi^2 \\ A=2900mi^2 \end{gathered}`

By substituting the values in the formula below, we will have

`\begin{gathered} \text{Population density=}\frac{population}{\text{area}} \\ \text{Population density}=\frac{12,620\text{people}}{2900mi^2} \\ \text{Population density}=4.352 \\ \text{Population density}\approx(nearest\text{ tenth)} \\ \text{Population density}=4.4\text{ } \end{gathered}`

Hence,

The population density is approximately 4.4 people per square mile